Explainable AI (XAI) methods generally fall into two categories. Post-hoc approaches generate explanations for pre-trained models and are compatible with various neural network architectures. These methods often use feature importance visualizations, such as saliency maps, to indicate which input regions influenced the model’s prediction. Unfortunately, they typically offer a coarse understanding of the model’s decision-making process. In contrast, ante-hoc (inherently explainable) methods rely on specially designed model architectures trained from scratch. A notable subclass of these methods provides explanations through prototypes, representative patches extracted from the training data. However, prototype-based approaches require dedicated architectures, involve specialized training procedures, and perform well only on specific datasets. In this work, we propose EPIC (Explanation of Pretrained Image Classification), a novel approach that bridges the gap between these two paradigms. Like post-hoc methods, EPIC operates on pre-trained models without architectural modifications. Simultaneously, it delivers intuitive, prototype-based explanations inspired by ante-hoc techniques. To the best of our knowledge, EPIC is the first post-hoc method capable of fully replicating the core explanatory power of inherently interpretable models. We evaluate EPIC on benchmark datasets commonly used in prototype-based explanations, such as CUB-200-2011 and Stanford Cars, alongside large-scale datasets like ImageNet, typically employed by post-hoc methods. EPIC uses prototypes to explain model decisions, providing a flexible and easy-to-understand tool for creating clear, high-quality explanations.

The main goal of Few-Shot learning algorithms is to enable learning from small amounts of data. One of the most popular and elegant Few-Shot learning approaches is Model-Agnostic Meta-Learning (MAML). In this paper, we propose a novel framework for Bayesian MAML called BH-MAML, which employs Hypernetworks for weight updates. It learns the universal weights point-wise, but a probabilistic structure is added when adapted for specific tasks. In such a framework, we can use simple Gaussian distributions or more complicated posteriors induced by Continuous Normalizing Flows.

Implicit neural representations (INR) have gained prominence for efficiently encoding multimedia data, yet their applications in audio signals remain limited. This study introduces the Kolmogorov-Arnold Network (KAN), a novel architecture using learnable activation functions, as an effective INR model for audio representation. KAN demonstrates superior perceptual performance over previous INRs, achieving the lowest Log-Spectral Distance of 1.29 and the highest Perceptual Evaluation of Speech Quality of 3.57 for 1.5~s audio. To extend KAN's utility, we propose FewSound, a hypernetwork-based architecture that enhances INR parameter updates. FewSound outperforms the state-of-the-art HyperSound, with a 33.3% improvement in MSE and 60.87% in SI-SNR. These results show KAN as a robust and adaptable audio representation with the potential for scalability and integration into various hypernetwork frameworks.

Training 3D generative models often faces bottle-necks due to dependencies on precise camera pose estimation, particularly when using Neural Radiance Fields (N eRFs) for photorealistic novel-view synthesis. We introduce HyperNeR-FGAN, a generative framework that eliminates camera pose requirements by integrating a hypernetwork with a Generative Adversarial Network (GAN). This architecture maps Gaussian noise directly to the weights of a NeRF model, bypassing viewing direction inputs during training. Our experiments demonstrate that HyperNeRFGAN achieves state-of-the-art performance on datasets where camera position estimation is impractical - notably in medical imaging scenarios with limited or ambiguous viewpoint metadata. Despite its architectural simplicity compared to existing methods, the model produces high-fidelity 3D reconstructions across diverse modalities, including MRI and X-ray-derived 2D scans. The framework's efficiency and robustness suggest broad applicability in domains requiring 3D generation from unstructured or poorly annotated 2D data. Key revisions emphasize the camera-pose independence, clinical relevance, and architectural efficiency while maintaining technical nrecision.

Classifier-free guidance (CFG) is an essential mechanism in contemporary text-driven diffusion models. In practice, in controlling the impact of guidance we can see the trade-off between the quality of the generated images and correspondence to the prompt. When we use strong guidance, generated images fit the conditioned text perfectly but at the cost of their quality. Dually, we can use small guidance to generate high-quality results, but the generated images do not suit our prompt. In this paper, we present β-CFG (β-adaptive scaling in Classifier-Free Guidance), which controls the impact of guidance during generation to solve the above trade-off. First, β-CFG stabilizes the effects of guiding by gradient-based adaptive normalization. Second, β-CFG uses the family of single-modal (β-distribution), time-dependent curves to dynamically adapt the trade-off between prompt matching and the quality of samples during the diffusion denoising process. Our model obtained better FID scores, maintaining the text-to-image CLIP similarity scores at a level similar to that of the reference CFG.

Implicit Neural Representations (INRs) have recently gained attention as a powerful approach for continuously representing signals such as images, videos, and 3D shapes using multilayer perceptrons (MLPs). However, MLPs are known to exhibit a low-frequency bias, limiting their ability to capture high-frequency details accurately. This limitation is typically addressed by incorporating high-frequency input embeddings or specialized activation layers. In this work, we demonstrate that these embeddings and activations are often configured with hyperparameters that perform well on average but are suboptimal for specific input signals under consideration, necessitating a costly grid search to identify optimal settings. Our key observation is that the initial frequency spectrum of an untrained model's output correlates strongly with the model's eventual performance on a given target signal. Leveraging this insight, we propose frequency shifting (or FreSh), a method that selects embedding hyperparameters to align the frequency spectrum of the model’s initial output with that of the target signal. We show that this simple initialization technique improves performance across various neural representation methods and tasks, achieving results comparable to extensive hyperparameter sweeps but with only marginal computational overhead compared to training a single model with default hyperparameters.

Implicit Neural Representations (INRs) approximate discrete data through continuous functions and are commonly used for encoding 2D images. Traditional image-based INRs employ neural networks to map pixel coordinates to RGB values, capturing shapes, colors, and textures within the network’s weights. Recently, GaussianImage has been proposed as an alternative, using Gaussian functions instead of neural networks to achieve comparable quality and compression. Such a solution obtains a quality and compression ratio similar to classical INR models but does not allow image modification. In contrast, our work introduces a novel method, MiraGe, which uses mirror reflections to perceive 2D images in 3D space and employs flat-controlled Gaussians for precise 2D image editing. Our approach improves the rendering quality and allows realistic image modifications, including human-inspired perception of photos in the 3D world. Thanks to modeling images in 3D space, we obtain the illusion of 3D-based modification in 2D images. We also show that our Gaussian representation can be easily combined with a physics engine to produce physics-based modification of 2D images. Consequently, MiraGe allows for better quality than the standard approach and natural modification of 2D images.

In practical applications of regression analysis, it is not uncommon to encounter a multitude of values for each attribute. In such a situation, the univariate distribution, which is typically Gaussian, is suboptimal because the mean may be situated between modes, resulting in a predicted value that differs significantly from the actual data. Consequently, to address this issue, a mixture distribution with parameters learned by a neural network, known as a Mixture Density Network (MDN), is typically employed. However, this approach has an important inherent limitation, in that it is not feasible to ascertain the precise number of components with a reasonable degree of accuracy. In this paper, we introduce CEC-MMR, a novel approach based on Cross-Entropy Clustering (CEC), which allows for the automatic detection of the number of components in a regression problem. Furthermore, given an attribute and its value, our method is capable of uniquely identifying it with the underlying component. The experimental results demonstrate that CEC-MMR yields superior outcomes compared to classical MDNs.

In computer graphics and vision, recovering easily modifiable scene appearance from image data is crucial for applications such as content creation. We introduce a novel method that integrates 3D Gaussian Splatting with an implicit surface representation, enabling intuitive editing of recovered scenes through mesh manipulation. Starting with a set of input images and camera poses, our approach reconstructs the scene surface using a neural signed distance field. This neural surface acts as a geometric prior guiding the training of Gaussian Splatting components, ensuring their alignment with the scene geometry. To facilitate editing, we encode the visual and geometric information into a lightweight triangle soup proxy. Edits applied to the mesh extracted from the neural surface propagate seamlessly through this intermediate structure to update the recovered appearance. Unlike previous methods relying on the triangle soup proxy representation, our approach supports a wider range of modifications and fully leverages the mesh topology, enabling a more flexible and intuitive editing process. The complete source code for this project can be accessed at github.com/WJakubowska/NeuralSurfacePriors.

Gaussian Splatting (GS) has recently emerged as an efficient representation for rendering 3D scenes from 2D images and has been extended to images, videos, and dynamic 4D content. However, applying style transfer to GS-based representations, especially beyond simple color changes, remains challenging. In this work, we introduce CLIPGaussian, the first unified style transfer framework that supports text- and image-guided stylization across multiple modalities: 2D images, videos, 3D objects, and 4D scenes. Our method operates directly on Gaussian primitives and integrates into existing GS pipelines as a plug-in module, without requiring large generative models or retraining from scratch. The CLIPGaussian approach enables joint optimization of color and geometry in 3D and 4D settings, and achieves temporal coherence in videos, while preserving the model size. We demonstrate superior style fidelity and consistency across all tasks, validating CLIPGaussian as a universal and efficient solution for multimodal style transfer.

Implicit field representations offer an effective way of generating 3D object shapes. They leverage an implicit decoder (IM-NET) trained to take a 3D point coordinate concatenated with a shape encoding and to output a value indicating whether the point is outside the shape. This approach enables the efficient rendering of visually plausible objects but also has some significant limitations, resulting in a cumbersome training procedure and empty spaces within the rendered mesh. In this paper, we introduce a new HyperCube architecture based on interval arithmetic that enables direct processing of 3D voxels, trained using a hypernetwork paradigm to enforce model convergence. The code is available at https://github.com/mproszewska/hypercube.

Over the past years, we have observed an abundance of approaches for modeling dynamic 3D scenes using Gaussian Splatting (GS). These solutions use GS to represent the scene's structure and the neural network to model dynamics. Such approaches allow fast rendering and extracting each element of such a dynamic scene. However, modifying such objects over time is challenging. SC-GS (Sparse Controlled Gaussian Splatting) enhanced with Deformed Control Points partially solves this issue. However, this approach necessitates selecting elements that need to be kept fixed, as well as centroids that should be adjusted throughout editing. Moreover, this task poses additional difficulties regarding the re-productivity of such editing. To address this, we propose Dynamic Multi-Gaussian Soup (D-MiSo), which allows us to model the mesh-inspired representation of dynamic GS. Additionally, we propose a strategy of linking parameterized Gaussian splats, forming a Triangle Soup with the estimated mesh. Consequently, we can separately construct new trajectories for the 3D objects composing the scene. Thus, we can make the scene's dynamic editable over time or while maintaining partial dynamics.

Conditional GANs are frequently used for manipulating the attributes of face images, such as expression, hairstyle, pose, or age. Even though the state-of-the-art models successfully modify the requested attributes, they simultaneously modify other important characteristics of the image, such as a person’s identity. In this paper, we focus on solving this problem by introducing PluGeN4Faces, a plugin to StyleGAN, which explicitly disentangles face attributes from a person’s identity. Our key idea is to perform training on images retrieved from movie frames, where a given person appears in various poses and with different attributes. By applying a type of contrastive loss, we encourage the model to group images of the same person in similar regions of latent space. Our experiments demonstrate that the modifications of face attributes performed by PluGeN4Faces are significantly less invasive on the remaining characteristics of the image than in the existing state-of-the-art models.

Many crucial problems in deep learning and statistical inference are caused by a variational gap, i.e., a difference between model evidence (log-likelihood) and evidence lower bound (ELBO). In particular, in a classical VAE setting that involves training via an ELBO cost function, it is difficult to provide a robust comparison of the effects of training between models, since we do not know a log-likelihood of data (but only its lower bound). In this paper, to deal with this problem, we introduce a general and effective upper bound, which allows us to efficiently approximate the evidence of data. We provide extensive theoretical and experimental studies of our approach, including its comparison to the other state-of-the-art upper bounds, as well as its application as a tool for the evaluation of models that were trained on various lower bounds.

Few-shot models aim at making predictions using a minimal number of labeled examples from a given task. The main challenge in this area is the one-shot setting where only one element represents each class. We propose HyperShot - the fusion of kernels and hypernetwork paradigm. Compared to reference approaches that apply a gradientbased adjustment of the parameters, our model aims to switch the classification module parameters depending on the task’s embedding. In practice, we utilize a hypernetwork, which takes the aggregated information from support data and returns the classifier’s parameters handcrafted for the considered problem. Moreover, we introduce the kernel-based representation of the support examples delivered to hypernetwork to create the parameters of the classification module. Consequently, we rely on relations between embeddings of the support examples instead of direct feature values provided by the backbone models. Thanks to this approach, our model can adapt to highly different tasks.*

Abstract Few-shot models aim at making predictions using a minimal number of labeled examples from a given task. The main challenge in this area is the one-shot setting, where only one element represents each class. We propose the general framework for few-shot learning via kernel HyperNetworks—the fusion of kernels and hypernetwork paradigm. Firstly, we introduce the classical realization of this framework, dubbed HyperShot. Compared to reference approaches that apply a gradient-based adjustment of the parameters, our models aim to switch the classification module parameters depending on the task’s embedding. In practice, we utilize a hypernetwork, which takes the aggregated information from support data and returns the classifier’s parameters handcrafted for the considered problem. Moreover, we introduce the kernel-based representation of the support examples delivered to hypernetwork to create the parameters of the classification module. Consequently, we rely on relations between the support examples’ embeddings instead of the backbone models’ direct feature values. Thanks to this approach, our model can adapt to highly different tasks. While such a method obtains very good results, it is limited by typical problems such as poorly quantified uncertainty due to limited data size. We further show that incorporating Bayesian neural networks into our general framework, an approach we call BayesHyperShot, solves this issue.

Designing a 3-D game scene is a tedious task that often requires a substantial amount of work. Typically, this task involves the synthesis and coloring of 3-D models within the scene. To lessen this workload, we can apply machine learning to automate some aspects of the game scene development. Earlier research has already tackled automated generation of the game scene background with machine learning. However, model autocoloring remains an underexplored problem. The automatic coloring of a 3-D model is a challenging task, especially when dealing with the digital representation of a colorful, multipart object. In such a case, we have to “understand” the object's composition and coloring scheme of each part. Moreover, existing single-stage methods have their caveats. We address these limitations by proposing a two-stage training approach to synthesize autocolored 3-D models. In the first stage, we obtain a 3-D point cloud representing a 3-D object, while in the second stage, we assign colors to points within such a cloud. Next, we generate a 3-D mesh in which the surfaces are colored based on the interpolation of colored points representing vertices of a given mesh triangle. This approach allows us to develop a smooth coloring scheme.

Most autoencoder-based generative machine learning models use a two-factor cost function composed of reconstruction error and prior distribution distance. The latter is often evaluated with kernel–based methods. We notice that the impact of the batch size is different on each of the factors: kernel distribution profits from larger batches, while the reconstruction term achieves peak performance on smaller ones. Thus, we define a batch size reconstruction-distribution trade-off. Instead of searching for an optimum global size of the batch, we propose to use small batches for the sake of reconstruction together with a vector enhanced with previously computed latent data for the sake of prior distribution optimization. We evaluate our method on standard benchmarks and illustrate that it can improve the model’s generative scores.

Most of the existing methods for estimating the local intrinsic dimension of a data distribution do not scale well to high dimensional data. Many of them rely on a non-parametric nearest neighbours approach which suffers from the curse of dimensionality. We attempt to address that challenge by proposing a novel approach to the problem: Local Intrinsic Dimension estimation using approximate Likelihood (LIDL). Our method relies on an arbitrary density estimation method as its subroutine, and hence tries to sidestep the dimensionality challenge by making use of the recent progress in parametric neural methods for likelihood estimation. We carefully investigate the empirical properties of the proposed method, compare them with our theoretical predictions, show that LIDL yields competitive results on the standard benchmarks for this problem, and that it scales to thousands of dimensions. What is more, we anticipate this approach to improve further with the continuing advances in the density estimation literature.

We introduce a new training paradigm that enforces interval constraints on neural network parameter space to control forgetting. Contemporary Continual Learning (CL) methods focus on training neural networks efficiently from a stream of data, while reducing the negative impact of catastrophic forgetting, yet they do not provide any firm guarantees that network performance will not deteriorate uncontrollably over time. In this work, we show how to put bounds on forgetting by reformulating continual learning of a model as a continual contraction of its parameter space. To that end, we propose Hyperrectangle Training, a new training methodology where each task is represented by a hyperrectangle in the parameter space, fully contained in the hyperrectangles of the previous tasks. This formulation reduces the NP-hard CL problem back to polynomial time while providing full resilience against forgetting. We validate our claim by developing InterContiNet (Interval Continual Learning) algorithm which leverages interval arithmetic to effectively model parameter regions as hyperrectangles. Through experimental results, we show that our approach performs well in a continual learning setup without storing data from previous tasks.

Scanning real-life scenes with modern registration devices typically give incomplete point cloud representations, mostly due to the limitations of the scanning process and 3D occlusions. Therefore, completing such partial representations remains a fundamental challenge of many computer vision applications. Most of the existing approaches aim to solve this problem by learning to reconstruct individual 3D objects in a synthetic setup of an uncluttered environment, which is far from a real-life scenario. In this work, we reformulate the problem of point cloud completion into an objects hallucination task. Thus, we introduce a novel autoencoder-based architecture called HyperPocket that disentangles latent representations and, as a result, enables the generation of multiple variants of the completed 3D point clouds. Furthermore, we split point cloud processing into two disjoint data streams and leverage a hypernetwork paradigm to fill the spaces, dubbed pockets, that are left by the missing object parts. As a result, the generated point clouds are smooth, plausible, and geometrically consistent with the scene. Moreover, our method offers competitive performances to the other state-of-the-art models, enabling a plethora of novel applications.

We propose OneFlow - a flow-based one-class classifier for anomaly (outlier) detection that finds a minimal volume bounding region. Contrary to density-based methods, OneFlow is constructed in such a way that its result typically does not depend on the structure of outliers. This is caused by the fact that during training the gradient of the cost function is propagated only over the points located near to the decision boundary (behavior similar to the support vectors in SVM). The combination of flow models and a Bernstein quantile estimator allows OneFlow to find a parametric form of bounding region, which can be useful in various applications including describing shapes from 3D point clouds. Experiments show that the proposed model outperforms related methods on real-world anomaly detection problems.

In this work, we propose a novel method for generating 3D point clouds that leverages the properties of hypernetworks. Contrary to the existing methods that learn only the representation of a 3D object, our approach simultaneously finds a representation of the object and its 3D surface. The main idea of our HyperCloud method is to build a hypernetwork that returns weights of a particular neural network (target network) trained to map points from prior distribution into a 3D shape. As a consequence, a particular 3D shape can be generated using point-by-point sampling from the prior distribution and transforming the sampled points with the target network. Since the hypernetwork is based on an auto-encoder architecture trained to reconstruct realistic 3D shapes, the target network weights can be considered to be a parametrization of the surface of a 3D shape, and not a standard representation of point cloud usually returned by competitive approaches. We also show that relying on hypernetworks to build 3D point cloud representations offers an elegant and flexible framework. To that point, we further extend our method by incorporating flow-based models, which results in a novel HyperFlow approach.

Most continual learning evaluations to date have focused on fully supervised image classification problems. This work for the first time extends such an analysis to the domain of 3D point cloud generation, showing that 3D object generators are prone to catastrophic forgetting along the same vein as image classifiers. Classic mitigation techniques, such as regularization and replay, are only partially effective in alleviating this issue. We show that due to the specifics of generative tasks, it is possible to maintain most of the generative diversity with a simple technique of uniformly sampling from different columns of a progressive neural network. While such an approach performs well on a typical synthetic class-incremental setup, more realistic scenarios might hinder strong concept separation by shifting task boundaries and introducing class overlap between tasks. Therefore, we propose an autonomous branch construction (ABC) method. This learning adaptation relevant to parameter-isolation methods employs the reconstruction loss to map new training examples to proper branches of the model. Internal routing of training data allows for a more effective and robust continual learning and generation of separate concepts in overlapping task setups.

This paper presents a mechanism for detecting adversarial examples based on data representations taken from the hidden layers of the target network. Individual autoencoders at intermediate layers of the target network are trained for this purpose. This describes the manifold of true data and, in consequence, can be used to classify whether a given example has the same characteristics as true data. It also gives insight into the behavior of adversarial examples and their flow through the layers of a deep neural network. Experimental results show that our method outperforms the state of the art in supervised and unsupervised settings.

Gaussian Processes (GPs) have been widely used in machine learning to model distributions over functions, with applications including multi-modal regression, time-series prediction, and few-shot learning. GPs are particularly useful in the last application since they rely on Normal distributions and enable closed-form computation of the posterior probability function. Unfortunately, because the resulting posterior is not flexible enough to capture complex distributions, GPs assume high similarity between subsequent tasks - a requirement rarely met in real-world conditions. In this work, we address this limitation by leveraging the flexibility of Normalizing Flows to modulate the posterior predictive distribution of the GP. This makes the GP posterior locally non-Gaussian, therefore we name our method Non-Gaussian Gaussian Processes (NGGPs). More precisely, we propose an invertible ODE-based mapping that operates on each component of the random variable vectors and shares the parameters across all of them. We empirically tested the flexibility of NGGPs on various few-shot learning regression datasets, showing that the mapping can incorporate context embedding information to model different noise levels for periodic functions. As a result, our method shares the structure of the problem between subsequent tasks, but the contextualization allows for adaptation to dissimilarities. NGGPs outperform the competing state-of-the-art approaches on a diversified set of benchmarks and applications.

In this work, we propose a novel method for generating 3D point clouds that leverage properties of hyper networks. Contrary to the existing methods that learn only the representation of a 3D object, our approach simultaneously finds a representation of the object and its 3D surfaces. The main idea of our HyperCloud method is to build a hyper network that returns weights of a particular neural network (target network) trained to map points from a uniform unit ball distribution into a 3D shape. As a consequence, a particular 3D shape can be generated using point-by-point sampling from the assumed prior distribution and transforming sampled points with the target network. Since the hyper network is based on an auto-encoder architecture trained to reconstruct realistic 3D shapes, the target network weights can be considered a parametrisation of the surface of a 3D shape, and not a standard representation of point cloud usually returned by competitive approaches. The proposed architecture allows to find mesh-based representation of 3D objects in a generative manner, while providing point clouds en pair in quality with the state-of-the-art methods.

The computation of the distance to the true distribution is a key component of most state-of-the-art generative models. Inspired by prior works on the Sliced-Wasserstein Auto-Encoders (SWAE) and the Wasserstein Auto-Encoders with MMD-based penalty (WAE-MMD), we propose a new generative model - a Cramer-Wold Auto-Encoder (CWAE). A fundamental component of CWAE is the characteristic kernel, the construction of which is one of the goals of this paper, from here on referred to as the Cramer-Wold kernel. Its main distinguishing feature is that it has a closed-form of the kernel product of radial Gaussians. Consequently, CWAE model has a~closed-form for the distance between the posterior and the normal prior, which simplifies the optimization procedure by removing the need to sample in order to compute the loss function. At the same time, CWAE performance often improves upon WAE-MMD and SWAE on standard benchmarks.

In many real binary classification problems, in addition to the presence of positive and negative classes, we are also given the examples of third neutral class, i.e., the examples with uncertain or intermediate state between positive and negative. Although it is a common practice to ignore the neutral class in a learning process, its appropriate use can lead to the improvement in classification accuracy. In this paper, to include neutral examples in a training stage, we adapt two variants of Tri-Class SVM (proposed by Angulo et al. in Neural Process Lett 23(1):89–101, 2006 ), the method designed to solve three-class problems with a use of single learning model. In analogy to classical SVM, we look for such a hyperplane, which maximizes the margin between positive and negative instances and which is localized as close to the neutral class as possible. In addition to original Angulo’s paper, we give a new interpretation of the model and show that it can be easily implemented in the primal. Our experiments demonstrate that considered methods obtain better results in binary classification problems than classical SVM and semi-supervised SVM.

Gaussian mixture models have many applications in density estimation and data clustering. However, the model does not adapt well to curved and strongly nonlinear data, since many Gaussian components are typically needed to appropriately fit the data that lie around the nonlinear manifold. To solve this problem, the active function cross-entropy clustering (afCEC) method was constructed. In this article, we present an online afCEC algorithm. Thanks to this modification, we obtain a method which is able to remove unnecessary clusters very fast and, consequently, we obtain lower computational complexity. Moreover, we obtain a better minimum (with a lower value of the cost function). The modification allows to process data streams.

We propose a general, theoretically justified mechanism for processing missing data by neural networks. Our idea is to replace typical neuron's response in the first hidden layer by its expected value. This approach can be applied for various types of networks at minimal cost in their modification. Moreover, in contrast to recent approaches, it does not require complete data for training. Experimental results performed on different types of architectures show that our method gives better results than typical imputation strategies and other methods dedicated for incomplete data.

Gaussian Mixture Models (GMM) have many applications in density estimation and data clustering. However, the models do not adapt well to curved and strongly nonlinear data, since many Gaussian components are typically needed to appropriately fit the data that lie around the nonlinear manifold. To solve this problem we constructed the Active Function Cross-Entropy Clustering (afCEC) method, which uses Gaussians in curvilinear coordinate systems. The method has a few advantages in relation to GMM: it enables easy adaptation to clustering of complicated data sets along with a predefined family of functions and does not need external methods to determine the number of clusters, as it automatically (on-line) reduces the number of groups. Experiments on synthetic data, Chinese characters, data from UCI repository and wind turbine monitoring systems show that the proposed nonlinear model typically obtains better results than the classical methods.

Clustering plays a basic role in many areas of data engineering, pattern recognition and image analysis. Gaussian Mixture Model (GMM) and Cross-Entropy Clustering (CEC) can approximate data of varied shapes by covering it with several clusters e.g. elliptical ones. However, it often happens that we need to extract clusters concentrated around lower dimensional non-linear manifolds. Moreover it is problematic to extract a cluster when data contains a big number of components. Here, we propose a method of solving the above problem by clustering density distribution. This approach allows to determine components of various sizes and geometry. Moreover, it is frequent in clustering problems that the data is naturally given by Gaussian distributions.